Question: Simplify the following expression: $ q = \dfrac{-3}{10} + \dfrac{3r}{-6r - 8} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-6r - 8}{-6r - 8}$ $ \dfrac{-3}{10} \times \dfrac{-6r - 8}{-6r - 8} = \dfrac{18r + 24}{-60r - 80} $ Multiply the second expression by $\dfrac{10}{10}$ $ \dfrac{3r}{-6r - 8} \times \dfrac{10}{10} = \dfrac{30r}{-60r - 80} $ Therefore $ q = \dfrac{18r + 24}{-60r - 80} + \dfrac{30r}{-60r - 80} $ Now the expressions have the same denominator we can simply add the numerators: $q = \dfrac{18r + 24 + 30r}{-60r - 80} $ $q = \dfrac{48r + 24}{-60r - 80}$ Simplify the expression by dividing the numerator and denominator by -4: $q = \dfrac{-12r - 6}{15r + 20}$